A222407 Digital roots of tribonacci numbers A000073.

0, 0, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1, 9, 9, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1, 9, 9, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1, 9, 9, 1, 1

Offset

0,5

Comments

From a(2) onwards, periodic with period length 39.

The period sums to 216 and contains no 3s. When divided into three sets of 13, further patterns are revealed in connection with A100402 (see link below). - Peter M. Chema, Dec 21 2016

Links

Table of n, a(n) for n=0..120.

Peter M. Chema, Period 39, divided into three sets of 13, with further digital root patterns

Formula

a(n) = A010888(A000073(n)). - Michel Marcus, Dec 19 2016

From Chai Wah Wu, Jan 30 2018: (Start)

a(n) = a(n-1) - a(n-3) + a(n-4) - a(n-6) + a(n-7) - a(n-9) + a(n-10) - a(n-12) + a(n-13) - a(n-15) + a(n-16) - a(n-18) + a(n-19) - a(n-21) + a(n-22) - a(n-24) + a(n-25) - a(n-27) + a(n-28) - a(n-30) + a(n-31) - a(n-33) + a(n-34) - a(n-36) + a(n-37) for n > 38.

G.f.: (-9*x^38 + 8*x^36 - 16*x^35 - x^34 + 15*x^33 - 20*x^32 + 4*x^31 + 12*x^30 - 17*x^29 + 10*x^27 - 17*x^26 - 2*x^25 + 10*x^24 - 15*x^23 + 3*x^22 + 3*x^21 - 11*x^20 + 2*x^19 + 2*x^18 - 5*x^17 - 4*x^16 + x^15 - x^14 - 4*x^13 - 4*x^12 - x^11 + x^10 - 5*x^9 - 5*x^8 + 2*x^7 - 3*x^6 - 3*x^5 - x^4 - x^2)/(x^37 - x^36 + x^34 - x^33 + x^31 - x^30 + x^28 - x^27 + x^25 - x^24 + x^22 - x^21 + x^19 - x^18 + x^16 - x^15 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 + x^4 - x^3 + x - 1). (End)

Maple

f:=proc(n) option remember; if n <= 1 then 0; elif n=2 then 1; else f(n-3)+f(n-2)+f(n-1); fi; end; # A000073
P:=n->if n=0 then 0 else ((n-1) mod 9) + 1; fi; # A010888
[seq(P(f(n)), n=0..200)];

Mathematica

FixedPoint[Total@ IntegerDigits@ # &, #] & /@ CoefficientList[ Series[x^2/(1 - x - x^2 - x^3), {x, 0, 81}], x] (* Michael De Vlieger, Dec 22 2016 *)
droot[n_]:=NestWhile[Total[IntegerDigits[#]]&, n, #>9&]; droot/@LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 150] (* or *) PadRight[{0, 0}, 150, {9, 9, 1, 1, 2, 4, 7, 4, 6, 8, 9, 5, 4, 9, 9, 4, 4, 8, 7, 1, 7, 6, 5, 9, 2, 7, 9, 9, 7, 7, 5, 1, 4, 1, 6, 2, 9, 8, 1}] (* Harvey P. Dale, Aug 21 2024 *)

Crossrefs

Cf. A000073, A010888, A210456.

Sequence in context: A198503 A129200 A074958 * A230724 A167280 A236629

Adjacent sequences: A222404 A222405 A222406 * A222408 A222409 A222410

Keyword

nonn

Author

N. J. A. Sloane, Feb 20 2013

Status

approved